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\title{An Efficient Quantum Computing Simulator using a Graphical Description for Many-Qbit Systems}
\subtitle{Simulation in the Stabilizer Formalism}
\author{Daniel Knüttel} 
\date{21.02.2020}
\institute{Universität Regensburg}

\titlegraphic{\small\center Universität Regensburg\\
    Faculty of the Institute of Theoretical Physics
    \vspace{-11mm}\flushright\includegraphics[height=1.0cm]{logo.png}}


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\begin{document}

\maketitle

\section{Introduction}

{
\begin{frame}{Motivation}

    \begin{itemize}
        \item Some (physical) problems are classically hard to solve.
        \item The quantum simulator: Mapping a hard problem to quantum hardware that can simulate this specific problem.
        \item The (universal) quantum computer: able to simulate any unitary transformation on the system.
    \end{itemize}

\end{frame}
}

{
\begin{frame}{Quantum Errors and Quantum Error Correction}
    \begin{itemize}
        \item Quantum systems at non-zero temperature often have dephasing effects and a finite population lifetime (relaxation).
        \item Fault tolerant QC needs a way to correct for those errors.
        \item Several strategies exist one important class of quantum error correction codes are \textbf{stabilizer codes}.
    \end{itemize}

\end{frame}
}

\section{Binary Quantum Computing}

{

\begin{frame}{Qbits}

    \begin{definition}
        A qbit is a two-level quantum mechanical system $\ket{0}, \ket{1}$ with $\braket{0}{1} = 0$.

        In the following $Z = \sigma_Z, X = \sigma_X, Y = \sigma_Y, I = \id$ will be used.
    \end{definition}
    
    Where $Z\ket{0} = +1\ket{0}$ and $Z\ket{1} = -1\ket{1}$.

    \begin{postulate}
        A $n$-qbit system is the tensor product of the single-qbit systems.
    \end{postulate}
    

\end{frame}
}
\end{document}
